Basics Of Retinal Image Quality

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2 Slide 2 Basics Of Retinal Image Quality

3 Slide 3 The optics of the eye are the first stage of vision. It is an extremely important stage but not the only stage.

4 Slide 4 Broadly There Are Two Components to the Visual System The optics - the focus of todays lecture; and Neural processing of the retinal image formed by the optics

5 Slide 5 Understanding the optics of the eye is key when imaging structures inside the eye. Understanding the optics and neural processing of the retina is key to understanding vision.

6 Eye s optics Photoreceptors Neural Processing Retinal image quality Sampling by the photo receptors Contrast Sensitivity function Visual Percept The Mind s Eye How one perceives what they see UH

7 Case 3 Mild NPDR, 50 yr, Male Courtesy Steve Burns 50 µm 50 µm Variance Map

9 Eye s optics Photoreceptors Neural Processing Optical quality (e.g., RMS WFE) Sampling by the photo receptors Contrast Sensitivity function Visual Percept The Mind s Eye How one perceives what they see UH

10 Slide 10 Sampling by Foveal Cones Projected Image Sampled Image 20/20 letter 5 arc minutes Courtesy Austin Roorda

11 Slide 11 Sampling by Foveal Cones Projected Image Sampled Image 20/5 letter 5 arc minutes Courtesy Austin Roorda

12 Eye s optics Photoreceptors Neural Processing Optical quality (e.g., RMS WFE) Sampling by the photo receptors Neural transfer function Visual Percept The Mind s Eye How one perceives what they see UH

14 Eye s optics Photoreceptors Neural Processing Optical quality (e.g., RMS WFE) Sampling by the photo receptors Contrast Sensitivity function Visual Percept The Mind s Eye How one perceives what they see UH

15 UH All is Vanity, By Gilbert

16 UH All Is Vanity, By Gilbert

17 Visual performance is dependent not only on retinal image quality but also on how the neural system processes the retinal image. The combination of retinal image quality and how the neural system processes the image results in a new set of image quality metrics referred to as visual image quality metrics. UH

18 We will focus today on retinal image quality Eye s optics Photoreceptors Neural Processing Retinal image quality Sampling by the photo receptors Contrast Sensitivity function Visual Percept The Mind s Eye How one perceives what they see

19 Slide 19 The optical quality of the retinal image is defined by pupil size and: Diffraction Wave Aberration Scatter Chromatic Aberration

20 Slide 20 The optical quality of the retinal image is defined by pupil size and: Diffraction Wave Aberration Scatter Chromatic Aberration

$Slide 21 Diffraction Any deviation of light rays from a rectilinear path which cannot be$

21 Slide 21 Diffraction Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction. Sommerfeld, ~

22 Slide 22 Wavefronts connect points having the same phase. Figure 5-1 from MacRae, Krueger and Applegate, Customized Corneal Ablation: The Quest for Super Vision, Slack, Inc

23 Slide 23 To understand diffraction, it is necessary to understand the behavior of a wavefront as it passes through an aperture or by edge.

24 This eye can see the light.

25 This eye cannot see the light.

26 Slide 26 But, the light can be dimly seen. Light is apparently bent by the aperture. How can this be explained?

$Slide 27 How can we explain diffraction?$

27 Slide 27 How can we explain diffraction? Use Huygen s Principle to explain how light bends around edges Each point on wavefront acts as a new source of light These new sources emit spherical wavefronts same velocity and frequency as original wavefront These new spherical wavefronts create a secondary wavefront Wavefront moves forward & process repeats Christiaan Huygens

28 Huygens postulated that every point on a wavefront was the source of a secondary wavefront.

29 For an unbounded system (no pupil), interference effects cause the light to propagate only in the original direction. Pupil unbounded bounded However, for a bounded wavefront (with pupil), the effects do not cancel.

30 Light from the wavelets can reach the eye even though a straight line from the eye to the point source does not pass through the aperture.

$Slide 31 A special and particularly interesting case of Fresnel diffraction, called Fraunhofer diffraction, occurs in the focal plane of an aberration-free or$

31 Slide 31 A special and particularly interesting case of Fresnel diffraction, called Fraunhofer diffraction, occurs in the focal plane of an aberration-free or nearly aberration-free imaging system. The Fraunhofer diffraction pattern of an axial point source defines the appearance of the point source in the image plane.

$Fraunhofer diffraction defines the diffraction$

32 Fraunhofer diffraction defines the diffraction limited point spread function (PSF). Airy disc

33 Diffraction - Circular Aperture Most relevant and important aperture shape Shape of most lenses & apertures (like the pupil!) For the eye - diffraction pattern is the image of a distant point source on the retina Also called Point Spread Function (PSF) Diffraction pattern (NO aberrations) consists of central bright spot (central maximum) Contains majority of light (~84%) dimmer rings surrounding central maximum Airy s Disk contains the central maximum

$Diffraction - Circular Aperture Diffraction$ Pedrotti. Introduction to Optics. 2nd Ed.

34 Diffraction - Circular Aperture Diffraction pattern Airy s Disk Aerial View Pedrotti & Pedrotti. Introduction to Optics. 2nd Ed. Prentice Hall; D View Hecht. Optics. 2nd Ed. Addison-Wesley; 1987.

35 Airy s Disk How large is Airy s Disk? d D θ r r = sinq = 1.22l d θ = angle between peak & first minimum (in radians) λ = wavelength (in m) d = diameter of circular aperture (in m) Sir George Biddel Airy: Inventor of spectacles for astigmatism

36 Slide 36 The radius of the Airy disc increases as pupil size decreases by the following formula. In length units as opposed to angular units f is the secondary focal length of the eye. r 1.22 f ' n is the index of image space n' a

37 Slide 37 As the radius of the Airy disk decreases the higher the fidelity of the retinal image. Said differently, in a perfect optical system the larger the pupil, the better the image.

38 Diffraction PSFs for pupil diameters mm 2 mm 3mm 4 mm 5 arc min. 5 mm 6 mm 7 mm 8 mm

39 Slide 39 Any scene is a collection of points. The image of a scene is represented by the point spread function of every point in the scene. So what we learn about a point image can be used to simulate the image of an object.

40 Slide 40 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 2.8 mm PSF 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 8.00 mm

41 Slide 41 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 5.6 mm 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 4.00 mm

42 Slide 42 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 11.2 mm 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 2.00 mm

43 Slide 43 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 22.4 mm 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 1.00 mm

44 Slide 44 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 44.8 mm 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 0.50 mm

45 Slide 45 Defocus = 0 D; RMS WFE = 0 mm Airy disc diameter = 89.6 mm 20/40 5 arc min. 20/20 20/12 Pupil Diameter = 0.25 mm

46 Slide 46 1 mm pin hole and aberrations UH

47 2.00 D 1.00 D 0.50 D 0.00 D

48 Slide 48 Is a 2 mm pin hole just as good for clinical use? UH

49 2.00 D 1.00 D 0.50 D 0.00 D

50 Slide 50 Do pin holes improve vision a lot?

51 Slide 51 For the eye with significant optical aberrations - Yes, but at a price. Decreasing the pupil for say a 5 mm diameter to 1mm decreases the light entering the eye by a factor of 25.

52 Slide 52 For the typical emmetropic eye (an eye with no spherical and astigmatic error) small pin holes decrease vision.

53 Patient with a 2.00 D refractive error and a drug dilated 8 mm pupil. 1 mm pupil placed in front of eye.

54 Patient with no refractive error and a drug dilated 8 mm pupil. 1 mm pupil placed in front of eye.

55 Slide 55 Clinical Implications of Diffraction Include: Diffraction fundamentally defines the upper limits of retinal image quality. Diffraction effects increase as pupil size decreases making the quality of the retinal image poorer and poorer. There is an optimal size for the clinical pinhole test around 0.75mm to 1.0mm.

56 Slide 56 The optical quality of the retinal image is defined by pupil size and: Diffraction Wave Aberration Scatter Chromatic Aberration

57 Simple Myopia

58 Simple Myopia with Optical Correction

59 Slide 59 In reality it is not so simple.

62 Slide 62 The eye has higher order wave aberrations that become increasingly manifest as the pupil diameter increases.

$Diffraction- Limited$ System Normal Eye

63 Slide 63 Diffraction- Limited System Normal Eye with Typical Aberrations 1mm 2mm 3mm 4mm Diffraction- Limited System Normal Eye with Typical Aberrations 5mm 6mm 7mm 8mm

64 Slide 64 For many clinical eyes (ie. keratoconics), it is important to correct the higher order aberrations. For the normal eye, the gains obtained by correcting higher order aberrations are primarily for large pupil sizes and diminish as the pupil size gets small.

65 Slide 65 In the past, a patient s eye which could not be corrected with conventional spherocylindrical corrections, was often dismissed with a diagnosis of irregular astigmatism. We are now in a position to attempt to correct these eyes.

66 Slide 66 Clinical Implications of Wave Aberrations for the Typical Normal Eye Include: The adverse effects on retinal image quality of wave aberrations in the normal healthy eye increase with pupil diameter. Retinal image quality has the highest fidelity for pupil diameters around 3mm in the typical well corrected eye. The effects of diffraction cause most well corrected eyes to see the same for pupil diameters < 2mm. Correlations between visual performance and wavefront aberrations must be made for the same pupil size.

67 Slide 67 The optical quality of the retinal image is defined by pupil size and: Diffraction Wave Aberration Scatter Chromatic Aberration

68 Slide 68 Back-scattered Forward-scattered Pupil

69 Slide 69 Type of scatter depends on particle size Rayleigh scatter For small particles (<< wavelength of light) Scatter Scatter is wavelength-dependent Short wavelengths are scattered more than longer wavelengths Tends to have uniform scattering in all directions 1 4 Tyndall (Mie) scatter Applies to larger particles (> wavelength of light) Scatter all visible wavelengths equally Forward scattering dominates Since all λ s scattered the same, causes object to look white (or some saturation of white)

70 Slide 70

71 Slide 71

72 Slide 72 20/25 VA Slitlamp Cross-section - Cataract Retro-Illumination - Cataract

73 Tom van den Berg

74 Tom van den Berg

75 Tom van den Berg

76 Ciliary corona Actual subjective appearance of straylight: a pattern of very fine streaks, not at all like the circularly uniform (Airy disclike) scattering pattern of particles of approximate wavelength size Tom van den Berg

77 Slide 77 Clinical Implications of Scatter Include: Despite the availability of a surgical cure, scatter resulting from cataract is the leading cause of legal blindness in the world. Scatter decreases image quality by washing out spatial detail in the retinal image.

78 Slide 78 The optical quality of the retinal image is defined by pupil size and: Diffraction Wave Aberration Scatter Chromatic Aberration

79 The speed of light in in the eye varies with the wavelength of light. The shorter the wavelength the slower the speed of light. Since the index of refraction is the ratio of the speed of light in a vacuum to the speed of light in the new medium, the index of refraction is greater for short wavelengths than it is for longer wavelengths.

80 Slide 80 As light enters the eye, the higher the refractive index the greater the angle of refraction as dictated by Snell s law. i n n' i' n sin i n' sin i'

81 The speed of light in a material is dependent on refractive index Most materials exhibit dispersion, or a change in the index of refraction with wavelength high n Positive chromatic aberration low short long What does dispersion imply about the following properties for different wavelengths in a material: Velocity velocity = c (speed of light) n l Shorter wavelengths: higher n slower velocity Slide courtesy of Jason Porter

82 The speed of light in a material is dependent on refractive index Most materials exhibit dispersion, or a change in the index of refraction with wavelength high n Positive chromatic aberration low short long What does dispersion imply about the following properties for different wavelengths in a material: Velocity i Angle of refraction n*sini = n' l *sini' n Shorter wavelengths: higher n smaller i greater refraction n' i' Slide courtesy of Jason Porter

83 The speed of light in a material is dependent on refractive index Most materials exhibit dispersion, or a change in the index of refraction with wavelength high n Positive chromatic aberration low short long What does dispersion imply about the following properties for different wavelengths in a material: Velocity Angle of refraction Power of a surface F = n' - n l r Shorter wavelengths: higher n higher power n i n' Slide courtesy of Jason Porter

84 Longitudinal (Axial) Chromatic Aberration

85 Slide 85 The difference in longitudinal chromatic aberration between 486 and 656 nm is just over 1 D. From 400 to 800 LCA is > 2 D. 1D Adapted from Bennet & Rabbetts, 1989

86 Transverse Chromatic Aberration

87 Slide 87 Clinical Implications of Chromatic Aberration Include: Chromatic aberration degrades the retinal image. The degradation in image quality is partially offset by the spectral sensitivities of the receptors. Chromatic aberration is capitalized on by the duochrome test. The adverse effects of low to moderate levels of mononchromatic aberrations are partially offset by chromatic aberration.

88 Slide 88 In summary, diffraction, chromatic aberration, wave aberrations, and scatter along with pupil diameter affect the optical quality of the retinal image.

89 Larry Thibos has written a basic level article on wavefront sensing and its advantages /The_2012_Charles_Prentice_Medal_Lecture.4.as px

90 Slide 90 Returning to Wavefront Error The specification of wavefront error. Why wavefront error is important in the design of ideal corrections. The advantage of specification of optical errors in terms of wavefront error as opposed to dioptric error.

91 Slide 91 To understand the need for the measurement of wavefront error in the correction of refractive errors, it is helpful to change our thinking from rays of light to waves of light.

92 Slide 92 Wavefronts Focus Rays Wavefront After Refraction

93 Slide 93 Waves Rays and Rays Ideal Aberrated

94 Slide 94 Wavefront error is the difference between the ideal wavefront and the actual wavefront.

95 Unaberrated Eye focused for distance Rays from distant object point, P. Slide courtesy Larry Thibos P perfect retinal image of object point Key points: All rays from P intersect at common point P on the retina. The optical distance from object P to image P is the same for all rays. Wavefront converging on retina is spherical.

96 Aberrated eye Rays from distant point source, P. P flawed retinal image Key points: Rays do NOT intersect at the same retinal location. The optical distance from object to retina is NOT the same for all rays. OPD = Optical Path Difference Wavefront is NOT spherical. Slide courtesy Larry Thibos

97 Slide 97 A particularly useful (but not the only) representation of ocular aberration is to fit the error between the actual wavefront and the ideal wavefront in three dimensions with a Zernike expansion. Fitting the error data with a Zernike expansion parcels the error into unique building blocks.

98 n m Z m n 2 3 Z 0 2 4

99 Z 0 0 Z m n -1 1 Z 1 Z 1 The 0 and 1 st radial orders of the Zernike expansion are generally ignored when measuring the monochromatic optical aberrations of the fixating eye. The reason is simple, neither affect the image quality of the fixating eye. The 0 radial order simply adds a constant to all locations and the 1 st radial order are prism terms affecting the position but not the optical quality of the image.

100 n m m Z n Z 2 Z 2 Z 2 The 2 nd radial order in the Zernike expansion the traditional ophthalmic prescription. 0 Z 2 reflect the spherical (defocus) error. and together reflect the cylindrical error. 1 Z 2 1 Z 2

101 n m Z m n Zernike Expansion modes in the 3 rd order and higher are collectively called the higher order aberrations.

102

103 n m Astigmatism Defocus Astigmatism Z m n 3 Trefoil Vertical Coma Horizontal Coma Trefoil 4 Tetrafoil Secondary Astigmatism Spherical Aberration Secondary Astigmatism Tetrafoil

104 Each mode s magnitude (weight) is defined by a coefficient C having the same subscript and superscript as the Zernike mode C Z C 4 = 0.3μ 4-2 C = 0.2μ C 4 = 0.1μ C 4 = 0.05μ -2 Four different magnitudes of secondary astigmatism.

105 = Weighted Zernike modes through the 4 th radial order in this PRK eye for a 6mm pupil are added together linearly to form the representation of the total wavefront error.

106 Angular Frequency Astigmatism Defocus Astigmatism 3 Trefoil Vertical Coma Horizontal Coma Trefoil 4 Tetrafoil Secondary Astigmatism Spherical Aberration Secondary Astigmatism Tetrafoil Sine Cosine

Vertical Coma Horizontal Coma Total Coma + = C 3-1 Z -1 3 C 3 1 Z 1 3 To determine the magnitude and orientation of any given aberration that has an angular frequency other than zero, the sine and

107 Vertical Coma Horizontal Coma Total Coma + = C 3-1 Z -1 3 C 3 1 Z 1 3 To determine the magnitude and orientation of any given aberration that has an angular frequency other than zero, the sine and cosine modes for the aberration of interest are added. For example, vertical coma (sine mode) and horizontal coma (cosine mode) can be added together to establish the total magnitude and orientation of coma.

can be added together, secondary astigmatism modes can be added

108 Thus, astigmatism modes can be added together, trefoil modes can be added together, coma modes can be added together, tetrafoil modes can be added together, secondary astigmatism modes can be added together, etc. n m = Sine Cosine

+ + + + Defocus Astigmatism Trefoil Coma

Spherical Aberration Total Aberration It

109 Defocus Astigmatism Trefoil Coma + + = Tetrafoil Secondary Astigmatism Spherical Aberration Total Aberration It can easily be seen that this post PRK eye aberrations are primarily dominated by coma, spherical aberration, secondary astigmatism, trefoil and a smaller amounts of defocus, astigmatism, and tetrafoil.

110 Slide 110 How are aberrations distributed in the population? and What is the best way to display ocular aberrations in a meaningful way?

111 The means of almost all Zernike modes are approximately zero and have a large intersubject variability Microns of Aberration Mean of 109 subjects 5.7 mm pupil Spherical aberration Z Z 3 Z Z3 Z4 Z4 Z Z 4 Z Z 5 Z Z 5 Z Z 5 Z Z 2 Z Z 2 Z Z 3 Z Z 3 Z4 Z4 Z Z 4 Z Z 5 Z Z 5Z Z 5 Z -5 5 Zernike Mode Porter et al., JOSA A (2001)

112 Slide 112 TINCO Study Patients age > 20 < 82; N = Coefficient Value in micrometers All Patients 7mm pupil C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 3rd 4th 5th 6th -0.6

113 Slide 113 The reason that the average coefficient value approaches zero is that for most modes of the Zernike expansion there are some eyes where the coefficient has a negative sign and in others it has a positive sign.

114 Slide 114 This similar to saying that the following group of individuals on average have no refractive error. Subject # Correction Subject # Correction Ave. = 0

115 Slide 115 On the other hand if we had looked at magnitudes we would have found the average magnitude of the refractive error to be 7.60 D not zero.

116 Slide 116 TINCO Study Patients age > 20 < 82; N = rd 4th 5th 6th Magnitude Wavefront Error in micrometers C6 C7 C8 0 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 All Patients 7mm pupil

117 Slide 117 Magnitude of the wavefront error for any Zernike mode is equivalent to the RMS wavefront error for that mode. RMS wavefront error for any term C 2 abs( C)

118 Slide 118 RMS wavefront error is equivalent to the standard deviation of the wavefront error over the pupil.

119 Angular Frequency Astigmatism Defocus Astigmatism 3 Trefoil Vertical Coma Horizontal Coma Trefoil 4 Tetrafoil Secondary Astigmatism Spherical Aberration Secondary Astigmatism Tetrafoil Sine Cosine

120 Slide 120 Sph. Ab TICO Study Patients age > 20 < 82; N = 113 Coefficient Value in micrometers rd Coma 4th C6 C7 C8 C9 C10 C11 C12 C13 C14 Trefoil 2 nd Astig. Tetrafoil

121 Slide 121 RMS error trefoil = RMS error coma = ( C C ) ( 3 ) ( C C ) ( 3) RMS error tetrafoil = RMS error 2 nd astig. = ( C C ) ( 4 ) ( C C ) ( 4 )

122 Slide 122 TICO Study Patients age > 20 < 82; N = 113 RMS Error in micrometers mm pupil Trefoil Coma Tetrafoil 2nd Astig Sph Ab

123 Slide 123 While RMS plots of each type of aberration tell us how much and which aberrations are contributing to the typical aberration structure, such plots do not tell us the orientation of the aberration, or how aberrations interact to increase or decrease visual performance.

124 Slide 124 Aberrations for any given person vary as a function of several factors including: Age Pupil diameter Tear quality between blinks Accommodation Optical disease and conditions that affect ocular optical quality (CLs, refractive surgery, IOLs, etc.)

125 Slide 125 The most common metric of wavefront aberration is total high order RMS wavefront error. RMS wavefront error is equivalent to the standard deviation of the high order wavefront over the pupil aperture. RMS ( C 3 3 ) 2 ( C 1 3 ) 2 ( C 1 3 ) 2 ( C 3 3 ) 2 ( C 4 4 ) 2...

126 Slide 126 RMS Wavefront Error in micrometers <40 40<60 60<80 0 3mm 4mm 5mm 6mm High order RMS aberration as a function of pupil size and age

127 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , Applegate

128 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , Figure 3A Applegate

129 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , Figure 3A Applegate

130 UH 2006 Applegate

131 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , 2007.

132 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , 2007.

133 These findings on the surface suggest that some of the decrease in acuity with age may be due to increase WFE with age. However -

Derived from data of B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, "Factors affecting light-adapted pupil size in normal human subjects," Invest Ophthalmol Vis Sci 35, 1132-7 (1994).

134 Derived from data of B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, "Factors affecting light-adapted pupil size in normal human subjects," Invest Ophthalmol Vis Sci 35, (1994). Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24: , Figure 1. UH 2006 Applegate

135 Slide 135 Optical signature of tear-film break-up Retro-illumination Fluorescein Aberrometer Before tears break Long after tears break Slide courtesy of Himebaugh, Begley and Thibos

136 Slide 136 Results of Quantitative Analysis Aberration map Scatter map Simulated image 20/20 20/20 Slide courtesy of Himebaugh, Begley and Thibos

137 Slide UHCO class of 2006 data

138 Normal Keratoconic

139 High order aberrations RE LE 2004 Applegate

140 Slide 140

3mm Patient with complaints 5.8mm Patient with complaints Δ ~ 3 letters 6/3.

141 3mm Patient with complaints 5.8mm Patient with complaints Δ ~ 3 letters 6/ mm Patient without complaints 6/4.5 6mm Patient without complaints Δ ~ 11 letters 6/12+2 6/4.8-2

142 Slide 142 Why is wavefront error important for designing corrections for the eye? Wavefront error defines the ideal compensating optic.

143 Slide 143 n speed of light in a vacuum speed of light in new optical media

144 Slide 144 Wavefront error is the key factor defining how much tissue or material to remove at every location. Wavefront retarded: Remove more material Wavefront advanced: Remove less material

145

146

147

148

149 Slide 149 Amount of materialto remove C WFE n' n Where: C = minimum amount of tissue to be removed WFE = wavefront error n = optical index of the material light is entering n = optical index of the material light is leaving

150 Slide 150 Wave aberration measurements are important to refractive surgery because: Wavefront error, adjusted for known biomechanical effects, details how much tissue to remove. Wavefront error after surgery reveals the effectiveness of the treatment. Wavefront error can be used to simulate the appearance of the retinal image. Wavefront error provides fundamental information needed to calculate other optical metrics of image quality such as the Modulation Transfer Function (MTF) and Point Spread Function (PSF).

151 Slide 151 Error WFE can be used to calculate the Point Spread Function WFE PSF RAA

152 n 2 3 PSF Astigmatism Defocus Astigmatism C n m m Z n m 4 Trefoil V. Coma H. Coma Trefoil 5 Quadrafoil 2 nd Astigmatism Spherical 2 nd Astigmatism Quadrafoil Pentafoil 2 nd Trefoil 2 nd V. Coma 2 nd H. Coma 2 nd Trefoil Pentafoil

153 Error Wavefront Error Point Spread Function Simulated Image

154 Arguably one of the most important results of optical theory in the 20 th century was to use the Fourier Theorem to link the PSF, LSF, MTF, PTF and OTF all together. (Goodman, JW 1968, Gaskill, JD) Joseph Fourier

155 Spatial Domain Frequency Domain Object Convolved with Fourier Transform WFE Object Spectrum Multiplied by MTF Point Spread Function = Image Fourier Transform Inverse Fourier Transform Inverse Fourier Transform Optical Transfer Function = Image Spectrum PTF

Aberrations and Visual Performance: Part I: How aberrations affect vision

Aberrations and Visual Performance: Part I: How aberrations affect vision Raymond A. Applegate, OD, Ph.D. Professor and Borish Chair of Optometry University of Houston Houston, TX, USA Aspects of this